Question for the Ex.Phys Boffin(s) (AWC, Power-Duration)

Possibly this is just a clarification of the question rather than an answer, but I thought:

1) the CP model itself breaks down at longer durations, because there is no power level which can be held indefinitely.
2) AWC represents work which can be done over and above that supplied by *critical power,* and as such it doesn't mean that the necessary energy is being supplied by anaerobic sources. The extra ~3w that AWC represents over the course of an hour is certainly still coming from aerobic sources, as you mention.
3) I can still punch it up to 400w+ for 30-60 seconds at the end of a 2hr SST ride, so the anaerobic energy is still there for access, but the multi-factorial muscle fatigue generally protests it's use.

frenchyge said:

2) AWC represents work which can be done over and above that supplied by *critical power,* and as such it doesn't mean that the necessary energy is being supplied by anaerobic sources. The extra ~3w that AWC represents over the course of an hour is certainly still coming from aerobic sources, as you mention.

Why/how is the extra ~3W coming from 'aerobic' sources? I guess you meant 'anaerobic'?

frenchyge said:

3) I can still punch it up to 400w+ for 30-60 seconds at the end of a 2hr SST ride, so the anaerobic energy is still there for access, but the multi-factorial muscle fatigue generally protests it's use.

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I would say that just means that you didn't try as hard as you could have during the 2hr effort, and hence still had some anaerobic capacity left to use in that 30-60secs.

Markster said:

Why/how is the extra ~3W coming from 'aerobic' sources? I guess you meant 'anaerobic'?

No, he meant aerobic: since critical power is below VO2max, you have to exceed critical power by more than a handful of watts before contribution from anaerobic energy sources is significant/required.

frenchyge said:

Possibly this is just a clarification of the question rather than an answer, but I thought:

1) the CP model itself breaks down at longer durations, because there is no power level which can be held indefinitely.
2) AWC represents work which can be done over and above that supplied by *critical power,* and as such it doesn't mean that the necessary energy is being supplied by anaerobic sources. The extra ~3w that AWC represents over the course of an hour is certainly still coming from aerobic sources, as you mention.
3) I can still punch it up to 400w+ for 30-60 seconds at the end of a 2hr SST ride, so the anaerobic energy is still there for access, but the multi-factorial muscle fatigue generally protests it's use.

Although I believe I understand what you say, with all due my respects, I believe that your statement is a bit confusing as well as probably not accurate.
If you talk about Anaerobic work capacity, then you cannot describe an aerobic metabolic state in your definition.
Determaning with such an accuracy, ~3w, that your source is aerobic seems to me extremely difficult...even to estimate it, especially when you talk about a course of an hour, which is done in the aerobic state, regardless of the intensity, unless, as you well say in your point 3 you sprint for 30-60 secs.

Cheers

Urkiola2 said:

If you talk about Anaerobic work capacity, then you cannot describe an aerobic metabolic state in your definition.

I think this is where distinguishing between anaerobic capacity as a physiological ability and anaerobic work capacity as a mathematical construct can be helpful. The latter is obviously meant to (and generally does) represent the former, but recognizing the fact that at their core they are really two different things helps explain such apparent discrepancies.

acoggan said:

I think this is where distinguishing between anaerobic capacity as a physiological ability and anaerobic work capacity as a mathematical construct can be helpful. The latter is obviously meant to (and generally does) represent the former, but recognizing the fact that at their core they are really two different things helps explain such apparent discrepancies.

I'm not sure that the OP ever really got an answer to his question, but I think the recent discussion does highlight the difficulty in trying to directly relate the physiological phenomena with the mathematical modelling, especially at the longer durations where even the math gets a little tenuous.

frenchyge said:

I'm not sure that the OP ever really got an answer to his question, but I think the recent discussion does highlight the difficulty in trying to directly relate the physiological phenomena with the mathematical modelling, especially at the longer durations where even the math gets a little tenuous.

No I haven't. I'm just being patient 🙂 ...

rmur17 said:

No I haven't. I'm just being patient 🙂 ...

You may be waiting a while for your answer. Take off your coat and stay a while.

rmur17 said:

But what happens when we get up to the following power-durations:

1. 10 MMP?
   
2. 15 MMP?
   
3. 20 MMP?
   
4. 30 MMP?
   
5. 60 MMP?
   
6. 120 MMP?
   
7. 240 MMP?
   

Rick, have you tried to fit Riegel's Endurance Equation to this data ?

amartinez said:

Rick, have you tried to fit Riegel's Endurance Equation to this data ?

whoops sorry I missed your post! What exactly might that be? :o

rmur17 said:

whoops sorry I missed your post! What exactly might that be? :o

A linear fit of Log(MMP) vs Log(Duration) in this range of duration, just curious how good would be the fit and the slope value.

amartinez said:

A linear fit of Log(MMP) vs Log(Duration) in this range of duration, just curious how good would be the fit and the slope value.

I don't know about the data that was posted but for a bit of fun I decided to do my own chart. He is a picture of my MMP from 2005/06 and 2006/07:

Alex Simmons said:

I don't know about the data that was posted but for a bit of fun I decided to do my own chart. He is a picture of my MMP from 2005/06 and 2006/07:

thanks for posting Alex. Pretty darned good fit over two seasons of data. Now, other than a high y-intercept and shallow slope being good things, what does it tell us? Ale et al? i don't see a magic % from 'AWC' bar on there 😄

rmur17 said:

thanks for posting Alex. Pretty darned good fit over two seasons of data. Now, other than a high y-intercept and shallow slope being good things, what does it tell us? Ale et al? i don't see a magic % from 'AWC' bar on there 😄

I just did a search for "Riegel Equation" and found these items of possible relevance. I have not read them yet.

run-down.comcalcs explained.phpOpen ↗

chef-de-race.comfatigue.htmOpen ↗

Hmmm.... Horse racing. Well, they are mammals. 🙂

The original article appears to be from American Scientist magazine (Volume 69, p 285)

Edit: AWC variations will be reflected in the intercept variations. Slope is related to CP/FTP. I guess I would expect that you might be able to gauge AWC contribution by looking goodness-of-fit numbers across the line, i.e., the fit should be better at higher durations due to lower AWC contribution out there. I think Excel will give you goodness-of-fit results if you have the Data Analysis package turned on.

rmur17 said:

thanks for posting Alex. Pretty darned good fit over two seasons of data. Now, other than a high y-intercept and shallow slope being good things, what does it tell us? Ale et al? i don't see a magic % from 'AWC' bar on there 😄

With my own data the fit also was quite good and I was curious of others (thanks Alex for your data), it could be useful to model longer durations for which the critical power model doesn't seem to work anymore.
The formula seems to work quite well for running and swimming.

The Slope is related to what Riegel called "Fatigue Factor" but I think it doesn't have a direct Ex.Phys. interpretation.

Anyway I don't have answers for your questions, no Ex.Phys Boffin here🙂

Quoted post said:

The formula was developed by Pete Riegel and published first in a slightly different form in Runner's World, August 1977, in an article in that issue entitled "Time Predicting." The formula was refined for other sports (swimming, bicycling, walking) in an article "Athletic Records and Human Endurance," also written by Pete Riegel, which appeared in American Scientist, May-June 1981.
run-down.comcalcs explained.phpOpen ↗

The article in American Scientist can be found her: Athletic Records and Human Endurance

amartinez said:

The Slope is related to what Riegel called "Fatigue Factor" but I think it doesn't have a direct Ex.Phys. interpretation.

FWIW, I would refer to it as "stamina" or "endurance", i.e., the extent to which one can avoid slowing down as duration progressively increases. (I would also hypothesize that changes in this slope are related to long-term CTL, but that's a bit of a different question.)

amartinez said:

The Slope is related to what Riegel called "Fatigue Factor" but I think it doesn't have a direct Ex.Phys. interpretation.

Oops. Yeah, you (and Andy) are right. I was thinking of the plot of energy vs. time where the slope is CP - the rate of change of energy vs. time is power - and didn't think. This is power vs. time (Ok, log transformed).

acoggan said:

FWIW, I would refer to it as "stamina" or "endurance", i.e., the extent to which one can avoid slowing down as duration progressively increases. (I would also hypothesize that changes in this slope are related to long-term CTL, but that's a bit of a different question.)

OK - I know that's another question but I just wanted to be clear what you mean by long term CTL.

How long it's been up there in the clouds and not having just ascended to that level perhaps?

acoggan said:

FWIW, I would refer to it as "stamina" or "endurance", i.e., the extent to which one can avoid slowing down as duration progressively increases. (I would also hypothesize that changes in this slope are related to long-term CTL, but that's a bit of a different question.)

Nice, lets call it ei=endurance index🙂, would be an insteresting value to track ?

A nice math property of this "endurance index" is it fully describe the "aspect/shape" of the power-duration relation for long(er) durations, when coupled with FT we could estimate any other MMP:

MMPt = FT * t^ei
where:
t is duration in hours
ei is the slope of the log(MMP)-log(Duration) relationship for (longer, >10' for ex.) durations (provided we have a good fit)

Just thinking in loud voice, are there real studies about this ?